The appearances of the same comet at different periods of it's return are so various, that we can never pronounce a given comet to be the same with one that has appeared before, from any peculiarities in it's physical aspect, as from it's color, magnitude, or shape; since, in all these respects, it is very different at different returns; but it is judged to be the same if it's path through the heavens, as traced among the stars, is the same.

The comet whose history is the most interesting, and which both of us have been privileged to see, is Halley's. Just before it's latest visit, in 1835, it's return was anticipated with so much expectation, not only by astronomers, but by all classes of the community, that a great and laudable eagerness universally prevailed, to learn the particulars of it's history. The best summary of these, which I met with, was given in the Edinburgh Review for April, 1835. I might content myself with barely referring you to that well-written article; but, as you may not have the work at hand, and would, moreover, probably not desire to read the whole article, I will abridge it for your perusal, interspersing some remarks of my own. I have desired to give you, in the course of these Letters, some specimen of the labors of astronomers, and shall probably never be able to find a better one.

It is believed that the first recorded appearance of Halley's comet was that which was supposed to signalize the birth of Mithridates, one hundred and thirty years before the birth of Christ. It is said to have appeared for twenty-four days; it's light is said to have surpassed that of the sun; it's magnitude to have extended over a fourth part of the firmament; and it is stated to have occupied, consequently, about four hours in rising and setting. In the year 323, a comet appeared in the sign Virgo. Another, according to the historians of the Lower Empire, appeared in the year 399, seventy-six years after the last, at an interval corresponding to that of Halley's comet. The interval between the birth of Mithridates and the year 323 was four hundred and fifty-three years, which would be equivalent to six periods of seventy-five and a half years. Thus it would seem, that in the interim there were five returns of this comet unobserved, or at least unrecorded. The appearance in the year 399 was attended with extraordinary circumstances. It was described in the old writers as a "comet of monstrous size and appalling aspect, it's tail seeming to reach down to the ground." The next recorded appearance of a comet agreeing with the ascertained period marks the taking of Rome, in the year 550,—an interval of one hundred and fifty-one years, or two periods of seventy-five and a half years having elapsed. One unrecorded return must, therefore, have taken place in the interim. The next appearance of a comet, coinciding with the assigned period, is three hundred and eighty years afterwards; namely, in the year 930,—five revolutions having been completed in the interval. The next appearance is recorded in the year 1005, after an interval of a single period of seventy-five years. Three revolutions would now seem to have passed unrecorded, when the comet again makes it's appearance in 1230. In this, as well as in former appearances, it is proper to state, that the sole test of identity of these cornets with that of Halley is the coincidence of the times, as near as historical records enable us to ascertain, with the epochs at which the comet of Halley might be expected to appear. That such evidence, however, is very imperfect, must be evident, if the frequency of cometary appearances be considered, and if it be remembered, that hitherto we find no recorded observations, which could enable us to trace, even with the rudest degree of approximation, the paths of those comets, the times of whose appearances raise a presumption of their identity with that of Halley. We now, however, descend to times in which more satisfactory evidence may be expected.

In the year 1305, a year in which the return of Halley's comet might have been expected, there is recorded a comet of remarkable character: "A comet of terrific dimensions made it's appearance about the time of the feast of the Passover, which was followed by a Great Plague." Had the terrific appearance of this body alone been recorded, this description might have passed without the charge of great exaggeration; but when we find the Great Plague connected with it as a consequence, it is impossible not to conclude, that the comet was seen by its historians through the magnifying medium of the calamity which followed it. Another appearance is recorded in the year 1380, unaccompanied by any other circumstance than its mere date. This, however, is in strict accordance with the ascertained period of Halley's comet.

We now arrive at the first appearance at which observations were taken, possessing sufficient accuracy to enable subsequent investigators to determine the path of the comet; and this is accordingly the first comet the identity of which with the comet of Halley can be said to be conclusively established. In the year 1456, a comet is stated to have appeared "of unheard of magnitude;" it was accompanied by a tail of extraordinary length, which extended over sixty degrees, (a third part of the heavens,) and continued to be seen during the whole month of June. The influence which was attributed to this appearance renders it probable, that in the record there is more or less of exaggeration. It was considered as the celestial indication of the rapid success of Mohammed the Second, who had taken Constantinople, and struck terror into the whole Christian world. Pope Calixtus the Second levelled the thunders of the Church against the enemies of his faith, terrestrial and celestial; and in the same Bull excommunicated the Turks and the comet; and, in order that the memory of this manifestation of his power should be for ever preserved, he ordained that the bells of all the churches should be rung at mid-day,—a custom which is preserved in those countries to our times.

The extraordinary length and brilliancy which was ascribed to the tail, upon this occasion, have led astronomers to investigate the circumstances under which its brightness and magnitude would be the greatest possible; and upon tracing back the motion of the comet to the year 1456, it has been found that it was then actually in the position, with respect to the earth and sun, most favorable to magnitude and splendor. So far, therefore, the result of astronomical calculation corroborates the records of history.

The next return took place in 1531. Pierre Appian, who first ascertained the fact that the tails of comets are usually turned from the sun, examined this comet with a view to verify his statement, and to ascertain the true direction of its tail. He made, accordingly, numerous observations upon its position, which, although rude, compared with the present standard of accuracy, were still sufficiently exact to enable Halley to identify this comet with that observed by himself.

The next return took place in 1607, when the comet was observed by Kepler. This astronomer first saw it on the evening of the twenty-sixth of September, when it had the appearance of a star of the first magnitude, and, to his vision, was without a tail; but the friends who accompanied him had better sight, and distinguished the tail. Before three o'clock the following morning the tail had become clearly visible, and had acquired great magnitude. Two days afterwards, the comet was observed by Longomontanus, a distinguished philosopher of the time. He describes its appearance, to the naked eye, to be like Jupiter, but of a paler and more obscured light; that its tail was of considerable length, of a paler light than that of the head, and more dense than the tails of ordinary comets.

The next appearance, and that which was observed by Halley himself, took place in 1682, a little before the publication of the 'Principia.' In the interval between 1607 and 1682, practical astronomy had made great advances; instruments of observation had been brought to a state of comparative perfection; numerous observatories had been established, and the management of them had been confided to the most eminent men in Europe. In 1682, the scientific world was therefore prepared to examine the visitor of our system with a degree of care and accuracy before unknown.

In the year 1686, about four years afterwards, Newton published his 'Principia,' in which he applied to the comet of 1680 the general principles of physical investigation first promulgated in that work. He explained the method of determining, by geometrical construction, the visible portion of the path of a body of this kind, and invited astronomers to apply these principles to the various recorded comets,—to discover whether some among them might not have appeared at different epochs, the future returns of which might consequently be predicted. Such was the effect of the force of analogy upon the mind of Newton, that, without awaiting the discovery of a periodic comet, he boldly assumed these bodies to be analogous to planets in their revolution round the sun.